To my knowledge, there aren't any NFL players with legitimate gymnastic experience. Still, I was able to come up with three freakish athletes who can do some crazy things with their bodies:

Jason Pierre-Paul, DE, New York Giants I have JPP scheduled to handle the floor exercise routine. As he proved in this video, he is a master of the backflip. Unfortunately, I don't think he could compete in any other events. (I'm not quite sure those rings would be able to hold him up ...)

Jerome Simpson, WR, Minnesota Vikings I have Simpson slated to handle the vault event. His epic front flip into the end zone against the Arizona Cardinals last season was all I needed to see. I've done my homework and think with a little bit of training Simpson would be fully capable of pulling off a Kasamatsu stretched with multiple twists or a Tsukahara double backs in a tuck and piked position. (They're impressive. Trust me.)

Darren Sproles, RB, New Orleans Saints I have yet to figure out which event would best suit the hyper-athletic Sproles, but I do like the fact that he'd actually be the same height as his competition. I'm open to any and all suggestions.